document.write( "Question 387318: use the properties of logarithms to elimate products, quotients and exponents from the following expression: log3[9 sqrt(x-5)/(x-1)^(5)] \r
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Algebra.Com's Answer #273984 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%283%2C+%28%289%2Asqrt%28x-5%29%29%2F%28x-1%29%5E5%29%29\"$
\n" ); document.write( "First we can use the property for quotients, $\"log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29\"$ , to split the single logarithm into the difference of the logarithms of the numerator and denominator:
\n" ); document.write( " $\"log%283%2C+%289%2Asqrt%28x-5%29%29%29+-+log%283%2C+%28%28x-1%29%5E5%29%29\"$
\n" ); document.write( "On the first logarithm we can use the property for products to split the logarithm of the product into the sum of the logarithms of its factors:
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\n" ); document.write( "Since square roots are the same as an exponent of 1/2 we can rewrite the second logarithm as a power of x-5:
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\n" ); document.write( "Now we can use the property for exponents to rewrite the last two logarithms:
\n" ); document.write( " $\"log%283%2C+%289%29%29+%2B+%281%2F2%29log%283%2C+%28x-5%29%29+-+5%2Alog%283%2C+%28x-1%29%29\"$
\n" ); document.write( "Last of all the first logarithm is one we can find (without a calculator). Since $\"9+=+3%5E2\"$ then the first logarithm must be 2:
\n" ); document.write( " $\"2+%2B+%281%2F2%29log%283%2C+%28x-5%29%29+-+5%2Alog%283%2C+%28x-1%29%29\"$
\n" ); document.write( "This is as far as we can go. \n" ); document.write( "

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